Question

Given △ R S T : R ( 6,1 ) , S ( 2, − 3 ) , T ( 7, − 5 ) and the transformation T ( x , y ) = ( − x , y ) , what kind of transformation is T?

a) Translation
b) Rotation
c) Reflection
d) Dilation

Answer 1

The transformation T(x, y) = (-x, y) is a reflection over the y-axis because it involves flipping the figure over this axis by changing the sign of the x-coordinate while keeping the y-coordinate the same.

Step-by-step explanation:

The transformation T(x, y) = (-x, y) described in the question is a type of geometric transformation where each point (x, y) of a figure is mapped to a new point (-x, y). This transformation has the effect of flipping the figure over the y-axis, as the x-coordinate of each point is multiplied by -1, thus reversing its direction on the x-axis, while the y-coordinate remains unchanged.

Therefore, the transformation T is a reflection over the y-axis. It is not a translation, rotation, or dilation, as those transformations do not involve flipping the figure over an axis but instead involve moving, rotating, or resizing the figure respectively.